Welcome to the forum! If you enter on a tourist visa, I assume immigration will not stop you because of outstanding taxes or unpaid CC payments, though they might remind you. Once you apply for a work or spousal visa, delinquent taxes will catch up with you. However, you should contact the city hall at your former place of residence as well as the credit card company and settle your debts.
If I were you, I'd contact the nearest Japanese embassy or consulate before embarking on the trip to be on the safe side.